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Prime Numbers/Transcript
Transcript Title text reads: The Mysteries of Life with Tim and Moby Moby is sitting in front of a control panel made up of various electronic gadgets. Tim approaches. TIM: Hey, what's going on? Moby beeps twice. TIM: Uh, you didn't say anything. Those were just beeps. Moby beeps three times. TIM: Are you feeling okay? Moby beeps five times. TIM: Wait. Two beeps, three beeps, five beeps… I see what you're doing. Let me guess, seven beeps is next? Moby beeps seven times. TIM: Man, I'm good. On-screen, a letter appears. Text reads as Tim narrates: Dear Tim and Moby, what are prime numbers? Thanks, Yovani. TIM: As you've noticed, Moby's been rattling off different numbers of beeps. Each of those numbers happens to be a prime number, which is a whole number greater than 1 that is divisible by exactly two numbers: 1 and itself. Numbers appear, reading: 2, 3, 5 and 7. TIM: Put another way, a prime number can only have two factors. A label appears, reading, factors. TIM: So 7 is a prime number, because it only has two factors: 1 and 7. An equation appears, reading, 7 equals 1 times 7. Moby beeps. TIM: Okay, I challenge you to find a number other than 1 or 7 that divides evenly into it! Moby blinks. TIM: Thought so. Okay, based on our definition, 1 can't be a prime number because it's only divisible by one number: 1. A number appears, reading, 1. It's crossed out. TIM: And a number like 8 is also not prime because it has four factors: 1, 8, 2, and 4. Two equations appear, reading: 8 equals 1 times 8; and, 8 equals 2 times 4. TIM: Numbers that are divisible by more than two numbers are called composite numbers. A label appears, reading, composite numbers. TIM: As for why Moby's beeping prime numbers, I'm not so sure. Moby beeps. TIM: Communicating with alien civilizations? Okay, you've been watching way too many sci-fi movies. The fact is, prime numbers have fascinated human civilization for as long as people have been studying math! We're pretty sure the ancient Egyptians knew about prime numbers; though the ancient Greeks were probably the first to really study them. On-screen, an ancient Egyptian puzzles over a sheet of papyrus. An ancient Greek shoves her aside. TIM: The famous Greek mathematician Euclid wrote an entire book on the subject! On-screen, Euclid appears. A label reads, Euclid. TIM: He wrote about some of the most fundamental properties of prime numbers. Moby beeps. TIM: Well, one of them was called the fundamental theorem of arithmetic. A label appears, reading, fundamental theorem of arithmetic. TIM: Here's what it says: every whole number greater than 1 that isn't a prime number is actually the product of prime numbers. In other words, by multiplying different sets of prime numbers together, you can come up with any non-prime number; no matter how big or small! Two equations appear, reading: 12 equals 2 times 2 times 3; and, 540 equals 2 times 2 times 3 times 3 times 3 times 5. TIM: That's one of the reasons mathematicians continue to study primes; they're like the building blocks of all numbers! Breaking any number down into its prime elements is a process called prime factorization. A label appears, reading, prime factorization. TIM: Euclid also proved that there are infinitely many prime numbers. On-screen, a long list of prime numbers appear, from 2 to 97. Moby beeps. TIM: Trust me, they just keep going! Now, you might be asking yourself how we came up with all those numbers. There's actually a pretty simple way to identify all the prime numbers up to a certain point, and it’s called the Sieve of Eratosthenes. A label appears, reading, Sieve of Eratosthenes. TIM: Eratosthenes was another ancient Greek mathematician who lived around the same time as Euclid. On-screen, Eratosthenes appears. A label reads, Eratosthenes. TIM: His technique for separating prime numbers from composite numbers is sort of like draining water from pasta. On-screen, Eratosthenes holds a strainer filled with noodles over a kitchen sink. TIM: First, we make a chart of every number from 1 to... say, 100. A chart appears, listing the numbers 1 through 100, in rows of ten. TIM: Since 1 isn't a prime, cross it out. On-screen, the number 1 is crossed out on the chart. TIM: Then circle 2, the smallest prime. On-screen, the number 2 is circled. TIM: Next, cross out every even number after 2; since they're all divisible by 2, they’re not prime. On-screen, all other even numbers are crossed out. TIM: Okay, then circle the next prime, 3, and cross out every third number, since they’re all divisible by 3. On-screen, the number 3 is circled. Every other third number is crossed out. TIM: Then circle 5, and cross out every fifth number. On-screen, the number 5 is circled. Every other fifth number is crossed out. TIM: Keep going until every number has been either circled or crossed out, and you’ve basically drained out all the composite numbers, leaving just the prime numbers behind! Of course, this only works up to a certain point; with bigger numbers, you’d eventually run out of space to write! Moby beeps. TIM: Not really. There’s no easy formula for generating prime numbers. The biggest prime numbers, numbers with millions of digits, can only be found using computers. On-screen, a computer printer spits out pages of numbers. TIM: As of August 2007, the largest known prime number was over 9 million digits long; and it took 700 computers about nine years to calculate! There are an infinite number of primes, of course, so mathematicians are always looking to raise the bar. There are even competitions that award big cash prizes to anybody who discovers the next biggest prime number. Moby beeps. Dollar signs appear in his eyes. TIM: No, you can't borrow my laptop for the next 10 years! Crazy robot. Category:BrainPOP Transcripts